| #voters | Their Vote |
|---|---|
| 40 | X>Y>Z |
| 20 | Y>Z>X |
| 40 | Z>Y>X |
A majority of the voters (20+40) rank X strictly bottom, so X should be an "irrelevant loser." But with Instant Runoff Voting (IRV), it isn't. IRV elects Y if X does not compete but elects Z if X does compete. This (essentially) actually happened in Louisiana 1991.
There are many other examples, but this is designed to illustrate that this can happen even if a majority of voters rank the loser dead last. E.g.
One can go further by creating artificial elections in which, e.g. H is ranked dead last by 99.9% of the voters, but plays a very important role. (With instant runoff voting: If H runs, then Z wins. If H drops out, then A wins.)
| #voters | their vote |
|---|---|
| 1000 | Z>...>H |
| 512 | P>A>...>H |
| 256 | Q>A>...>H |
| 128 | R>A >...>H |
| 64 | S>A>...>H |
| 32 | T>A>...>H |
| 16 | U>A>...>H |
| 8 | V>A>...>H |
| 4 | W>A>...>H |
| 2 | X>A>...>H |
| 1 | Y>A>...>H |
| 2 | H>A |
Similar example but for Borda voting